This is a follow up on Specify radius of an arc with pgfplots and axis direction cs? If I'd like to change the MWE from there to the following:
\pgfplotsset{compat=1.10}
\begin{tikzpicture}
\begin{axis}[
xmin=-20,xmax=20,
]
\addplot{x}; % not important, just to make things show up
\end{axis}
\draw (axis cs:-16,0) arc[start angle=180, end angle=0, radius=8]; % <-- want to keep units of coordinate system here
\end{tikzpicture}
How can I specify the arc radius in axis coordinate system?
What I already tried was a solution given in Extract x, y coordinate of an arbitrary point in TikZ using \pgfextractx.
This leads to wrong lengths in my case.

axisenvironment. Theaxis cs:part is not needed since pgfplots 1.11 IIRC. – Manuel Dec 19 '14 at 11:09